Question

At what time (to nearest second) immediately after 4 o'clock do the hands of a clock coincide?

• A. 04:20:00 o'clock
• B. 04:20:45 o'clock
• C. 04:21:49 o'clock
• D. 04:21:55 o'clock

Hint:

To calculate when the clock hands coincide, use the formula \( T = \frac{60 \times h}{11} \), where \( h \) is the hour.

Answer 1

The Correct Option is C

Step 1: Clock Hands Coincidence Principle.
The hour and minute hands of a clock align every \( 5 \frac{5}{11} \) minutes. Therefore, the duration between coincidences subsequent to 4 o'clock is computed as: \[ T = \frac{60 \times 4}{11} = 218 \, \text{minutes} \, 49.1 \, \text{seconds}. \] Consequently, the approximate time of alignment after 4 o'clock is \( 04:21:49 \).

Final Answer: \[ \boxed{04:21:49 \, \text{o'clock}} \]